Automobile Max Load--Cargo Volume Regression PA
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West Chester University of Pennsylvania *
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303
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Industrial Engineering
Date
Jan 9, 2024
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docx
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Uploaded by ChancellorCaribou3914
Automobile Max Load/Cargo Volume Regression PA
Complete the following. Do the analysis in Excel and enter all requested results and explanations into this
document.
Submit this document with your solutions as either a Word file or a PDF to the associated Assignments drop box.
No other file types will be accepted.
Also submit your Excel work.
1.
Suppose we are interested in determining how much the cargo volume a vehicle has affects the maximum load the
vehicle is rated for. Download the dataset
Auto2008 REVISED.xlsx
and do a complete analysis of this potential
relationship.
A.
First construct a scatter plot of the two data series. Copy and pasted the plot as a picture below:
B.
Now calculate the covariance and the correlation coefficient and report them here:
Covariance:
2746.4578
Correlation:
0.7422
C.
Discuss the potential relationship between Max Load and Cargo Volume (CV) as indicated by the scatter plot and
the covariance and correlation coefficient: Fairly strong positive relationship between Max Load and Cargo
Volume.
2.
Now do an ordinary least squares regression (OLS) to see if the maximum load a vehicle is rated for is impacted by
the cargo volume and to what degree. The population model is:
0
1
o
M
u
ax Load
Cargo V l me
f
CV
Run the regression using a 90% confidence level and report your results by copying the output tables from
Excel and pasting them as pictures below:
A.
Report the following individually:
b
0
=
664.2910
b
1
=
11.1020
R
2
=
0.5509
B.
Is the regression model as a whole statistically significant in explaining any of the behavior of the Max Load
variable?
Yes
Explain what you based your answer on:
Reject the null hypothesis that Beta1 = 0, as the p
value for the test is much smaller than our alpha of 10%.
C.
At a 10% significance level, are the slope and the intercept each statistically significant?
Beta
0
=
Yes
Beta
1
=
Yes
D.
Explain how you determined the answer for each:
Reject the separate null hypotheses that Beta0 = 0, and
Beta1 = 0, as the p value for each test is much smaller than our alpha of 10%.
E.
Given these regression results, what is the average impact of a one cubic foot increase in cargo volume on the
maximum load a vehicle is rated for? Explain in detail, making use of the estimated 90% confidence interval for
the slope term:
Each additional cubic foot of cargo volume adds 11.1020 pounds to the maximum load a
vehichle is rated for. We are 90% confident that the true impact additional cubis foot of cargo
volume is the addition of in between 9.8268 and 12.3773 pounds.
F.
What is the R
2
telling us?
55.09% of the variation in maximum load A VEHICLE CAN HANDLE IS EXPLAINED BY THE AMOUNT OF CARGO
VOLUME A VEHICLE HAS
G.
What is the prediction equation obtained from this regression?
ˆ
Y
664.2910+11.1020 *CV
H.
What is the expected load capacity of a vehicle with 29 cubic feet of cargo volume?
|
29
E Max Load CV
986.2501
3.
Now copy and paste as pictures both the residual plot and the normal probability plot:
Complete a residual analysis of the L.I.N.E. assumptions (see NOTES, pages 8 and 9):
L: Potentially a random around zero, indicating linearity. However, the waviness and possible nonlinearity
with the quadratic trend line suggests that linearity may be questionable.
I: If we have violation of linearity, we also already see lack independence. This is primarily due to the
waviness that we clearly see in the scatter plot, although it is not as pronounced in the residual plot.
N: The distribution of the residuals has long tails relative to a normal distribution, so the results from the
hypothesis tests for significance are somewhat unreliable.
E: The spread of the residuals seems fairly constant for the most part, indicating no violation of the
homoskedasticity assumption.
4.
Now summarize your regression results with respect to whether they are good or not. Make sure to include a
statement of how well your model explains differences in maximum load variation across different vehicles:
Looked good until I did the residual plot analysis, then I saw some potential problems with the significance test
results of the model.
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